On A Priori Statistics in Minimum-Variance Estimation Problems

Abstract

Simple general formulas are derived for investigating the effect of errors in a priori statistics on the minimum-variance estimates of linear regression parameters from observations obscured by noise. These formulas permit a direct evaluation of the covariance matrix of the errors of a posteriori estimates, showing the sensitivity to errors in a priori weighting matrix. A simple example illustrates that, for slight variations in the assumed a priori statistics, the calculated a posteriori error standard deviations of the estimates can deviate substantially from the correct values.